INDEX unsymmetrical

Carbonates are indexed in Chemicaly hstracts under carbonic acid, esters. Symmetrical diesters have the prefix di or bis. Unsymmetrical diesters are listed with the two radicals following each other. For example, ethyl phenyl carbonic diester is C2H OCOOC H. Table 6 Hsts commonly used carbonates, their Chemicaly hstracts Service Registry Number, and formulas. 

In general, it may be said that enantiomers have identical properties in a symmetrical environment, but their properties may differ in an unsymmetrical environment. Besides the important differences previously noted, enantiomers may react at different rates with achiral molecules if an optically active catalyst is present they may have different solubilities in an optically active solvent., they may have different indexes of refraction or absorption spectra when examined with circularly polarized light, and so on. In most cases these differences are too small to be useful and are often too small to be measured. 

The Cluj-distance index CJD is obtained from the symmetric Cluj-distance matrix CJD as the sum of the matrix entries corresponding to all the P order paths (i.e. bonds) above the main diagonal, i.e. applying the Wiener operator "iPto the P order sparse symmetric Cluj-distance matrix CJD or from the sparse unsymmetric Cluj-distance matrix CJDjj applying the Wiener orthogonal operator "W ... 

The Cluj-detour index CJA is analogously obtained from the P order sparse symmetric Cluj-detour matrix CJA applying the Wiener operator IV or from the unsymmetric Cluj-detour matrix CJAu applying the Wiener orthogonal operator VF ... 

This is a molecular descriptor proposed with the aim of quantifying the chirality of a molecule by means of the positive or negative quantification of the chirality of the environment of the atoms in the molecule for any scalar atomic property [Moreau, 1997]. The basic idea is that unsymmetrical environments are not the privilege of atoms in chiral molecules, however they are the most frequent situations. The Moreau chirality index is defined as... 

Selecting different combinations of Mi and M2 matrices leads to the derivation of several Schultz-type indices. The original Schultz molecular topological index MTI is obtained for Ml = A and M2 = D, where D is the topological —> distance matrix. Typical Schultz indices are derived from (D, A, D), A, D ), (W, A, D), (W A, D ), (W, A, W), (UCJ, A, UCJ), (USZ, A, USZ), where is the reciprocal distance matrix, W is one among —> walk matrices, is the reciprocal walk matrix, UCJ and USZ the unsymmetrical Cluj and Szeged matrices, respectively. 

Unsymmetrical, symmetric edge- and hyper-Szeged index for ethylbenzene, respectively. 

Unlike matrix MM, which usually is unsymmetrical, the matrix H is symmetric and related to MM by a similarity transformation, so that H and MM have the same eigenvalues and interrelated eigenvectors. The matrix H is also related to the Laplacian matrix moreover, the half sum of the elements of H coincides with the Randic connectivity index ... 

For instance, for any graph, the hyper-Wiener index can be calculated by applying the Wiener operator to the symmetric path-Cluj distance matrix SCJD or the orthogonal Wiener operator to the unsymmetrical path-Cluj distance matrix UCJDp. 

The effective index represents the dimensionless in-plane component of the propagation vector of the mode (the propagation vectors are in units of A being the vacuum wavelength). The optical modes can be characterized as transversal electric (TE the electric field is polarized in-plane) and transversal magnetic (TM the magnetic field is polarized in-plane). For unsymmetric slab waveguides, a minimum thickness (cutoff) exists for each mode to appear [48]. 

If the path-Wiener matrix, W, is substituted by the unsymmetric Cluj matrix, then the unsymmetric expanded vertex-distance matrix is obtained. This has been used for a new definition of the hyper-Wiener index (Diudea and Gutman, 1998 Ivanciuc et al, 1998 Gutman, 2004). This kind of expanded vertex-distance matrix of T2 is shown below ... 

The half sum of entries in the SZe/p matrix gives the Szeged index SZ, and the hyper-Szeged index SZp, respectively. The difference between SZp and SZe gives the SZ matrix SZa = SZp — SZe- -The unsymmetric Cluj matrix, CJu, was defined on the basis of the numbers N, and Ny. 

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